A pneumatic tire for motorcycle has inherent advantages and disadvantages depending on whether the carcass of the tire has a bias structure or a radial structure. When the carcass has the radial structure, it is deemed that the tire has a problem in a linear traveling property at high speed. The liner traveling property is a resistance property and a converging property to lateral force that is inevitably input from a road surface in traveling, and a tire, which has a smaller degree of vibration caused by external disturbance and can recover the thus caused vibration more promptly, is more excellent in the liner traveling property. To overcome the problem inherent to the radial structure, the applicant has proposed in patent document 1 an pneumatic tire for motorcycle having a radial carcass structure that can exhibit an excellent liner traveling property, Further, the applicant has also proposed in patent document 2 a pneumatic radial tire for motorcycle which can improve a motion performance including turning force at corners, a limit of grip, recovery of overall vibration behaviors of a vehicle body, a slip control property, a road surface irregularity absorbing property, and steering stability and can be applied to a front wheel or a rear wheel by using spiral belts and angled belts together and making use of the advantageous characteristics of the respective belts.    Patent document 1: Japanese Examined Patent Application Publication No. 7-41764    Patent document 2: Japanese Unexamined Patent Application Publication No. 2004-67058